Depth Optimization of Ansatz Circuits Enables Efficient Variational Quantum Algorithms for Fluid Dynamics

The growing complexity of quantum circuits poses a significant challenge to realising practical quantum computation, as the inherent fragility of qubits introduces errors that accumulate with increasing circuit depth. Spyros Tserkis, Muhammad Umer, and Dimitris G. Angelakis investigate methods to overcome this limitation, demonstrating that the depth of circuits used in variational quantum algorithms can be substantially reduced. Their approach introduces additional qubits alongside mid-circuit measurements and classically controlled operations, allowing for more efficient computation. By applying this technique to model nonlinear dynamics, specifically the one-dimensional Burgers’ equation relevant to computational fluid dynamics, the researchers show that their circuits accurately represent fluid flow in both stable and chaotic conditions, and crucially, offer advantages in noisy quantum systems where gate errors are relatively low compared to qubit idling errors.

The increasing depth of quantum circuits presents a major limitation for the execution of quantum algorithms, as the limited coherence time of physical qubits leads to noise that manifests as errors during computation. This work focuses on circuits relevant to variational quantum algorithms and demonstrates that their depth can be reduced by introducing additional qubits, mid-circuit measurements, and classically controlled operations. In particular, the team shows that these non-unitary quantum circuits achieve a significant reduction in circuit depth while maintaining accuracy in simulating the Burgers’ equation, offering a pathway to overcome limitations imposed by qubit coherence.

Shallow Circuits via Non-Unitary Quantum Computation

This research presents a novel approach to designing quantum circuits, successfully reducing their complexity without sacrificing accuracy. The team achieved this by incorporating additional qubits, strategically placed mid-circuit measurements, and operations controlled by classical computation. This method proves particularly effective for simulating complex systems, as demonstrated by its application to the one-dimensional Burgers’ equation, a cornerstone of computational fluid dynamics. Traditional quantum circuits rely on unitary operations, which can become increasingly susceptible to noise as the circuit deepens.

This work explores non-unitary circuits, offering a pathway to shallower designs. The team demonstrates that these circuits can achieve significant reductions in depth while maintaining the necessary accuracy for simulating fluid dynamics, effectively mitigating the impact of noise on quantum computations. The research establishes a clear advantage for non-unitary circuits when two-qubit gate error rates are lower than idling error rates, highlighting the importance of tailoring circuit designs to the specific characteristics of the quantum hardware. Analysis of error budgets reveals a linear scaling of errors with the number of qubits for non-unitary circuits, contrasting with the quadratic scaling observed in unitary circuits, suggesting potential for improved scalability. The team also developed a benchmark for assessing circuit fidelity, providing a means to compare the performance of different circuit designs even when simulating large circuits is computationally prohibitive. This research represents a significant step towards developing more robust and efficient quantum algorithms for complex simulations.

Variational Quantum Algorithms for Optimization Problems

Variational quantum algorithms (VQAs) hold promise for leveraging near-term quantum computers to solve complex optimization problems. These algorithms combine quantum computation with classical optimization techniques, but their performance can be limited by the barren plateau phenomenon, where the gradient of the cost function vanishes, hindering efficient optimization. This research investigates a novel approach to mitigate the barren plateau and improve the performance of VQAs. The team’s method focuses on tailoring circuit designs to specific hardware capabilities, optimizing for the dominant error sources to enhance performance and scalability. Through numerical simulations on benchmark problems, they demonstrate that their approach significantly improves the optimization landscape and achieves faster convergence and higher solution accuracy compared to existing VQA implementations. These results suggest a pathway towards realizing the full potential of VQAs for tackling real-world optimization challenges.

Shorter Circuits Model Fluid Dynamics Effectively

This research demonstrates a novel approach to quantum circuit design, achieving reductions in circuit depth through the strategic addition of qubits, mid-circuit measurements, and classically controlled operations. The team successfully applied this method to represent nonlinear dynamics, specifically modelling fluid flow configurations relevant to computational fluid dynamics in both laminar and turbulent states. Results indicate that these non-unitary circuits offer advantages over traditional unitary circuits in scenarios where two-qubit gate error rates are lower than idling error rates. The study establishes a benchmark for assessing circuit fidelity, providing a means to compare the performance of different circuit designs even when simulating large circuits is computationally prohibitive.

Analysis of error budgets reveals a linear scaling of errors with the number of qubits for non-unitary circuits, contrasting with the quadratic scaling observed in unitary circuits, suggesting potential for improved scalability. Importantly, the team found that the relative performance of unitary and non-unitary circuits depends on the specific error characteristics of the quantum hardware, with unitary circuits performing best under low idling error and non-unitary circuits excelling when two-qubit gate errors are minimized. This research represents a significant step towards developing more robust and efficient quantum algorithms for complex simulations.